Question: Simplify; express your answer in exponential form. Assume $p\neq 0, q\neq 0$. $\dfrac{{p^{3}}}{{(p^{-3}q^{5})^{-4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{3}}$ to the exponent ${1}$ . Now ${3 \times 1 = 3}$ , so ${p^{3} = p^{3}}$ In the denominator, we can use the distributive property of exponents. ${(p^{-3}q^{5})^{-4} = (p^{-3})^{-4}(q^{5})^{-4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{p^{3}}}{{(p^{-3}q^{5})^{-4}}} = \dfrac{{p^{3}}}{{p^{12}q^{-20}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{3}}}{{p^{12}q^{-20}}} = \dfrac{{p^{3}}}{{p^{12}}} \cdot \dfrac{{1}}{{q^{-20}}} = p^{{3} - {12}} \cdot q^{- {(-20)}} = p^{-9}q^{20}$.